Line tart pan with parchment paper.
In a small saucepan, over medium heat, cook sugar, honey, marmalade and apple juice, stirring until sugar is dissolved. Bring to a boil, then turn down heat and simmer until mixture begins to thicken, about 2 minutes; set aside.
Peel and core the apples. Cut into thin wedges then sprinkle with lemon juice to prevent discoloration. Add apples to syrup in pot and toss to coat. Simmer, covered, 15 minutes. Uncover and simmer on low heat until apples are very soft, 10 to 15 minutes more. Stir occasionally to prevent sticking.
Transfer apple mixture to a glass bowl and allow to cool to room temperature. Cover with plastic wrap and chill in refrigerator 2 hours.
For the Tart: Combine flour and sugar in bowl of electric mixer. Add butter and, starting at low speed, stir until pieces of flour-covered butter are cut into tiny particles. Stop machine to check consistency. Add egg yolks and blend until particles are moistened, add water and blend until dough comes together. Don't over mix or dough will be tough. Wrap in waxed paper or plastic wrap and refrigerate 5 minutes.
Remove one-fourth of dough and refrigerate. Flatten remaining dough into thin round disk and press into 11-inch tart pan with removable bottom. On a floured board, roll out remaining one-fourth dough into 12-inch square. Using a fluted pastry cutter or knife, cut into 16 to 18 (1/2-inch) strips. Chill 10 minutes.
Spread Filling evenly in pastry-lined tart pan. Arrange 1/2 of dough strips across top of filling, spacing as evenly as possible. Arrange remaining strips in opposite direction, across first strips of dough, making a lattice pattern. Cut off strips even with edge of pan and press each strip with bottom pastry and pinch to seal.
Place tart on baking sheet and bake at 375 degrees until golden brown, 1 hour. Remove from oven and set on rack to cool. Remove from tart pan by carefully loosing bottom from sides of pan.